The most appropriate tool to measure cellular response at large deformations is atomic force microscopy (AFM) [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}, [11]}.
AFM cantilevers with pyramidal tips, colloidal probes, or flat geometries are used to indent or compress cells.
Therefore, a common approach to characterize the elasticity of cells utilizes the Hertzian theory, which describes the contact between two linear elastic solids [12]}, but is limited to the range of small deformations [13]}.
Experimental measurements with medium-to-large deformations typically show significant deviations from the Hertz prediction, e. g., for cells or hydrogel particles [14]}.
Instead of linear elasticity, a suitable description of cell mechanics for bioprinting applications requires more advanced hyperelastic material properties.
While for simple anucleate fluid-filled cells such as, e.g., red blood cells, theoretical models abound [15]}, [16]}, [17]}, [18]}, [19]}, the availability of models for cells including a complex cytoskeleton is rather limited.
In axisymmetric geometries, [20]} and [21]} used an axisymmetric finite element model with neo-Hookean hyperelasticity to model AFM and microchannel experiments on biological cells.
In shear flow, approximate analytical treatments are possible [22]}, [23]}, [24]}, [25]}.
Computationally, [23]} carried out 2D simulations while in 3D [27]} utilized a DPD technique based on a bead-spring model. Furthermore, [28]}, [29]} presented an arbitrary Lagrangian-Eulerian approach for elastic particles in viscoelastic fluids.
Finally, [30]} and [31]} considered viscoelastic and neo-Hookean finite element models, respectively, in shear flow.
